The present invention relates in general to three-dimensional (3-D) display of tomographic data, and more specifically to preventing leaks from an object of interest into other unwanted objects during extraction of the object using a connectivity method.
Tomographic medical imaging employs the collection of data representing cross sections of a body. A plurality of object interrogations can be processed mathematically to produce representations of contiguous cross-sectional images. Such cross-sectional images are of great value to the medical diagnostician in a non-invasive investigation of internal body structure. Techniques employed to collect the data are, for example, x-ray computed tomography (CT), nuclear magnetic resonance imaging (MR), single photon emission tomography, positron emission tomography, or ultrasound tomography.
A body to be imaged exists in three dimensions. Tomographic devices process data for presentation as a series of contiguous cross-sectional slices along selectable axes through the body. Each cross-sectional slice is made up of a number of rows and columns of voxels (parallelepiped volumes with certain faces corresponding to pixel spacing within each slice and others corresponding to slice spacing), each represented by a digitally stored number related to a computed signal intensity in the voxel. In practice, an array of, for example, 64 slices may each contain 512 by 512 voxels. In normal use, a diagnostician reviews images of a number of individual slices to derive the desired information. In cases where information about a surface within the body is desired, the diagnostician relies on inferences of the 3-D nature of the object derived from interrogating the cross-sectional slices. At times, it is difficult or impossible to attain the required inference from reviewing contiguous slices. In such cases, a synthesized 3-D image is desired.
Synthesizing a 3-D image from tomographic data is a two-step process. In the first step, a mathematical description of the desired object is extracted from the tomographic data. In the second step, the image is synthesized from the mathematical description.
Dealing with the second step first, assuming that a surface description can be synthesized from knowledge of the slices, the key is to go from the surface to the 3-D image. The mathematical description of the object is made up of the union of a large number of surface elements (SURFELS). The SURFELS are operated on by conventional computer graphics software, having its genesis in computer-aided design and computer-aided manufacturing, to apply surface shading to objects to aid in image interpretation through a synthesized two-dimensional image. The computer graphics software projects the SURFELS onto a rasterized image and determines which pixels of the rasterized image are turned on, and with what intensity or color. Generally, the shading is lightest (i.e., most intense) for image elements having surface normals along an operator-selected line of sight and successively darker for those elements inclined to the line of sight. Image elements having surface normals inclined more than 90 degrees from the selected line of sight are hidden in a 3-D object and are suppressed from the display. Foreground objects on the line of sight hide background objects. The shading gives a realistic illusion of three dimensions.
Returning now to the first step of extracting a mathematical description of the desired surface from the tomographic slice data, this step is broken down into two substeps, namely the extraction (i.e., identification) of the object from the rest of the tomographic data, and the fitting of a surface to the extracted object. A surface is fitted to the object by giving a mathematical description to the boundary between the voxels of the object and any non-object voxels. The description can be obtained using the marching cubes, dividing cubes, or cuberille methods, for example. The dividing cubes method is described in U.S. Pat. No. 4,719,585, issued to Cline et al. on Jan. 12, 1988, which is incorporated by reference.
In the dividing cubes method, the surface of interest is represented by the union of a large number of directed points. The directed points are obtained by considering in turn each set of eight cubically adjacent voxels in the data base of contiguous slices. Gradient values are calculated for the cube vertices using difference equations. Each large cube formed in this manner is tested to determine whether the object boundary passes through it. One way to perform this test is to compare the density (i.e., intensity value) at each vertex with a threshold value (or a range between two threshold values) defining the object. If some densities are greater and some less than the threshold (or some within the range and some not), then the surface passes through the large cube. This process will be referred to as thresholding whether using a single threshold or a range (e.g., upper and lower thresholds).
In the event that the surface passes through the large cube, then the cube is subdivided to form a number of smaller cubes, referred to as subcubes or subvoxels. By interpolation of the adjacent point densities and gradient values, densities are calculated for the subcube vertices and a gradient is calculated for the center of the subcube. The densities are tested (e.g., compared to the threshold). If the surface passes through a subcube, then the location of the subcube is output with its normalized gradient, as a directed point. The union of all directed points generated by testing all subcubes within large cubes through which the surface passes, provides the surface representation. The directed points are then rendered (i.e., rasterized) for display on a CRT, for example.
In general, the thresholding method works very well when the voxels corresponding to an object-of-interest are substantially the only ones in the tomographic data that fall within the particular thresholding range (i.e., are the only occupants of the particular neighborhood in the image histogram). This is true of bone in CT and blood vessels in MR, for example. However, many potential objects-of-interest within a body share a density range (or other identifying property), such as various organs in CT measurements. Thresholding alone cannot distinguish between such objects in the same range or having the same property.
A method known as connectivity can be used to separate objects that occupy the same neighborhood in a histogram. In using connectivity, only voxels connected to a user-identified seed voxel in the object-of-interest will be considered during the surface extraction step. A voxel is connected to the seed if and only if (1) the voxel is a neighbor of the seed or a neighbor of another connected voxel, and (2) the voxel shares a specified property (e.g., falling within the same threshold range) with the seed voxel. Connectivity has been successfully used in generating 3-D CT images of soft tissue structures such as the knee ligaments.
A particular problem encountered with the connectivity method is the possibility of leaks. Consider, for example, the application of connectivity to a tomographic set of 2-D images in which two objects need to be separated which are in close proximity. Because of system imperfections such as finite bandwidth, partial volume, field inhomogeneities and additive noise, a small bridge might exist between the two objects making it possible that the connectivity algorithm might leak from one object to the other and cause the two objects to be considered as one.
Several methods have been proposed to prevent leaks. One method is to have a user manually identify bridges before the connectivity algorithm is applied. This method is tedious and difficult to apply for inter-slice bridges. Another method is to circumscribe the object-of-interest with a user-defined bounding volume like a rectangular parallelepiped. This method does not work well for irregularly shaped objects (e.g., most internal organs). Another method operates by redefining the criteria for being connected. Thus, by specifying that a certain number of voxels have to overlap before they are considered to be neighbors, certain types of leaks can be plugged.
None of the prior-art methods are satisfactory for wide-spread application to medical images because each either fails in certain circumstances or is difficult and inconvenient to implement. The prior-art methods can be combined empirically to plug leaks in a wider class of cases. However, there still exist cases where the methods fail individually or collectively.
Accordingly, it is a principal object of the present invention to provide a method and apparatus for preventing leaks when applying connectivity to identify an object-of-interest in tomographic image data.
It is another object of the invention to construct a three-dimensional image of an object-of-interest from two-dimensional tomographic data using connectivity without leaks to unwanted objects.
It is a further object of the invention to provide method and apparatus to prevent leaks during application of connectivity to tomographic data with minimal reliance on user input.